Finite Group DatabasebetaFinite Group DatabasebetaOrder 12352.
310 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 157 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×Dic386 | C2 | semidirect |
| 3. #20259864 | C2 | semidirect |
| 4. D4×Dic193 | C2 | semidirect |
| 5. C4×C22⋊D193 | C2 | semidirect |
| 6. #20259859 | C2 | semidirect |
| 7. #20259857 | C2 | semidirect |
| 8. #20259855 | C2 | semidirect |
| 9. C2×C4×Dic193 | C2 | semidirect |
| 10. C42×D193 | C2 | semidirect |
| 11. C4×D4×C193 | C2 | semidirect |
| 12. #15690554 | C4 | direct (N × H) |
| 37. Dic386 | C2×C4 | semidirect |
| 38. C22⋊D193 | C2×C4 | semidirect |
| 40. C2×Dic193 | C2×C4 | semidirect |
| 48. C4×D193 | C2×C4 | semidirect |
| 50. D4×C193 | C2×C4 | semidirect |
| 66. C4×C193 | #41 | semidirect |
| 71. Dic193 | #41 | semidirect |
| 77. C193 | C4×#41 | semidirect |
| 85. C4×D4 | D193 | semidirect |
| 118. D4 | C4×D193 | semidirect |
| 149. C4 | #15690554 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690554 | 2 |
| C4×Dic386 | 2 |
| #20259864 | 2 |
| D4×Dic193 | 2 |
| C4×C22⋊D193 | 2 |
| #20259859 | 2 |
| #20259857 | 2 |
| #20259855 | 2 |
| C2×C4×Dic193 | 2 |
| C42×D193 | 2 |
| C4×D4×C193 | 2 |
| C4×#41 | 193 |